How Do You Derive the Constructive Interference Equation for Reflection?

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SUMMARY

The discussion focuses on deriving the equation for constructive interference in reflection, specifically 2t = (n + 1/2)(λ/n), where λ represents the wavelength and n is the index of refraction. Participants emphasize the importance of including a diagram to illustrate the concept clearly. The equation is confirmed as correct for constructive interference, which occurs when the path difference is a half-integer multiple of the wavelength.

PREREQUISITES
  • Understanding of wave interference principles
  • Familiarity with the concept of wavelength (λ)
  • Knowledge of the index of refraction
  • Ability to create and interpret diagrams in physics
NEXT STEPS
  • Study the principles of wave interference in more depth
  • Learn about the derivation of the index of refraction in different media
  • Explore the applications of constructive interference in optics
  • Practice drawing and analyzing diagrams related to wave behavior
USEFUL FOR

Students studying physics, particularly those focusing on optics and wave phenomena, as well as educators looking for clear explanations of interference concepts.

baileya
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Homework Statement


Derive the equation 2t=(n+1/2)(lamba/index of refraction) to show it's the correct eq'n for constructive interference on reflection. Include a diagram.


Homework Equations


2t=(n+1/2)(lambda/index of refraction)


The Attempt at a Solution


I'm not sure how you'd show it's the correct eq'n...
 
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hi baileya! :smile:

(have a lambda: λ :wink:)
baileya said:
… Include a diagram.

I'm not sure how you'd show it's the correct eq'n...

you'd draw a diagram! :wink:

what does it show? :smile:
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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